Cyrillic numerals are a numeral system derived from the Cyrillic script, developed in the First Bulgarian Empire in the late 10th century. It was used by South and East Slavic peoples; the system was used in Russia as late as the early 18th century, when Peter the Great replaced it with Arabic numerals as part of his civil script reform initiative. Cyrillic numbers played a role in Peter the Great's currency reform plans, with silver wire kopecks issued after 1696 and mechanically minted coins issued between 1700 and 1722 inscribed with the date using Cyrillic numerals. By 1725, Russian Imperial coins had transitioned to Arabic numerals; the Cyrillic numerals may still be found in books written in the Church Slavonic language. The system is a quasi-decimal alphabetic system, equivalent to the Ionian numeral system but written with the corresponding graphemes of the Cyrillic script; the order is based on the original Greek alphabet rather than the standard Cyrillic alphabetical order. A separate letter is assigned to each unit, each multiple of ten, each multiple of one hundred.
To distinguish numbers from text, a titlo is sometimes drawn over the numbers, or they are set apart with dots. The numbers are written as pronounced in Slavonic from the high value position to the low value position, with the exception of 11 through 19, which are written and pronounced with the ones unit before the tens. Examples: – 1706 – 7118To evaluate a Cyrillic number, the values of all the figures are added up: for example, ѰЗ is 700 + 7, making 707. If the number is greater than 999, the thousands sign is used to multiply the number's value: for example, ҂Ѕ is 6000, while ҂Л҂В is parsed as 30,000 + 2000, making 32,000. To produce larger numbers, a modifying sign is used to encircle the number being multiplied. Two scales existed in such cases, one giving a new name and sign every order of magnitude, the other, each squaring except for the end Glagolitic numerals are similar to Cyrillic numerals except that numeric values are assigned according to the native alphabetic order of the Glagolitic alphabet.
Glyphs for the ones and hundreds values are combined to form more precise numbers, for example, ⰗⰑⰂ is 500 + 80 + 3 or 583. As with Cyrillic numerals, the numbers 11 through 19 are written with the ones digit before the glyph for 10. Whereas Cyrillic numerals use modifying signs for numbers greater than 999, some documents attest to the use of Glagolitic letters for 1000 through 6000, although the validity of 3000 and greater is questioned. Early Cyrillic alphabet Glagolitic alphabet Relationship of Cyrillic and Glagolitic scripts Greek numerals Combining Cyrillic Millions
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal positional numeral system; the numerals are made up of three symbols. For example, thirteen is written as three dots in a horizontal row above two horizontal bars. With these three symbols each of the twenty vigesimal digits could be written. Numbers after 19 were written vertically in powers of twenty; the Mayan used powers of twenty, just as the Hindu–Arabic numeral system uses powers of tens. For example, thirty-three would be written as one dot, above three dots atop two bars; the first dot represents "one twenty" or "1×20", added to three dots and two bars, or thirteen. Therefore, + 13 = 33. Upon reaching 202 or 400, another row is started; the number 429 would be written as one dot above one dot above four dots and a bar, or + + 9 = 429. Other than the bar and dot notation, Maya numerals were sometimes illustrated by face type glyphs or pictures; the face glyph for a number represents the deity associated with the number.
These face number glyphs were used, are seen on some of the most elaborate monumental carving. Adding and subtracting numbers below 20 using Maya numerals is simple. Addition is performed by combining the numeric symbols at each level: If five or more dots result from the combination, five dots are removed and replaced by a bar. If four or more bars result, four bars are removed and a dot is added to the next higher row. With subtraction, remove the elements of the subtrahend symbol from the minuend symbol: If there are not enough dots in a minuend position, a bar is replaced by five dots. If there are not enough bars, a dot is removed from the next higher minuend symbol in the column and four bars are added to the minuend symbol, being worked on; the "Long Count" portion of the Maya calendar uses a variation on the vigesimal numbering. In the second position, only the digits up to 17 are used, the place value of the third position is not 20×20 = 400, as would otherwise be expected, but 18×20 = 360, so that one dot over two zeros signifies 360.
This is because 360 is the number of days in a year. Subsequent positions use all twenty digits and the place values continue as 18×20×20 = 7,200 and 18×20×20×20 = 144,000, etc; every known example of large numbers in the Maya system uses this'modified vigesimal' system, with the third position representing multiples of 18×20. It is reasonable to assume, but not proven by any evidence, that the normal system in use was a pure base-20 system. Several Mesoamerican cultures used similar numerals and base-twenty systems and the Mesoamerican Long Count calendar requiring the use of zero as a place-holder; the earliest long count date is from 36 BC. Since the eight earliest Long Count dates appear outside the Maya homeland, it is assumed that the use of zero and the Long Count calendar predated the Maya, was the invention of the Olmec. Indeed, many of the earliest Long Count dates were found within the Olmec heartland. However, the Olmec civilization had come to an end by the 4th century BC, several centuries before the earliest known Long Count dates—which suggests that zero was not an Olmec discovery.
Mayan numerals were added to the Unicode Standard in June, 2018 with the release of version 11.0. The Unicode block for Mayan Numerals is U+1D2E0–U+1D2FF: Maya Mathematics - online converter from decimal numeration to Maya numeral notation. Anthropomorphic Maya numbers - online story of number representations. BabelStone Mayan Numerals - free font for Unicode Mayan numeral characters
Hindu–Arabic numeral system
The Hindu–Arabic numeral system is a positional decimal numeral system, is the most common system for the symbolic representation of numbers in the world. It was invented between the 4th centuries by Indian mathematicians; the system was adopted in Arabic mathematics by the 9th century. Influential were the books of Al-Kindi; the system spread to medieval Europe by the High Middle Ages. The system is based upon ten glyphs; the symbols used to represent the system are in principle independent of the system itself. The glyphs in actual use are descended from Brahmi numerals and have split into various typographical variants since the Middle Ages; these symbol sets can be divided into three main families: Western Arabic numerals used in the Greater Maghreb and in Europe, Eastern Arabic numerals used in the Middle East, the Indian numerals used in the Indian subcontinent. The Hindu-Arabic numerals were invented by mathematicians in India. Perso-Arabic mathematicians called them "Hindu numerals", they came to be called "Arabic numerals" in Europe, because they were introduced to the West by Arab merchants.
The Hindu–Arabic system is designed for positional notation in a decimal system. In a more developed form, positional notation uses a decimal marker, a symbol for "these digits recur ad infinitum". In modern usage, this latter symbol is a vinculum. In this more developed form, the numeral system can symbolize any rational number using only 13 symbols. Although found in text written with the Arabic abjad, numbers written with these numerals place the most-significant digit to the left, so they read from left to right; the requisite changes in reading direction are found in text that mixes left-to-right writing systems with right-to-left systems. Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, most of which developed from the Brahmi numerals; the symbols used to represent the system have split into various typographical variants since the Middle Ages, arranged in three main groups: The widespread Western "Arabic numerals" used with the Latin and Greek alphabets in the table, descended from the "West Arabic numerals" which were developed in al-Andalus and the Maghreb.
The "Arabic–Indic" or "Eastern Arabic numerals" used with Arabic script, developed in what is now Iraq. A variant of the Eastern Arabic numerals is used in Urdu; the Indian numerals in use with scripts of the Brahmic family in India and Southeast Asia. Each of the dozen major scripts of India has its own numeral glyphs; as in many numbering systems, the numerals 1, 2, 3 represent simple tally marks. After three, numerals tend to become more complex symbols. Theorists believe that this is because it becomes difficult to instantaneously count objects past three; the Brahmi numerals at the basis of the system predate the Common Era. They replaced the earlier Kharosthi numerals used since the 4th century BC. Brahmi and Kharosthi numerals were used alongside one another in the Maurya Empire period, both appearing on the 3rd century BC edicts of Ashoka. Buddhist inscriptions from around 300 BC use the symbols that became 1, 4, 6. One century their use of the symbols that became 2, 4, 6, 7, 9 was recorded.
These Brahmi numerals are the ancestors of the Hindu–Arabic glyphs 1 to 9, but they were not used as a positional system with a zero, there were rather separate numerals for each of the tens. The actual numeral system, including positional notation and use of zero, is in principle independent of the glyphs used, younger than the Brahmi numerals; the place-value system is used in the Bakhshali Manuscript. Although date of the composition of the manuscript is uncertain, the language used in the manuscript indicates that it could not have been composed any than 400; the development of the positional decimal system takes its origins in Hindu mathematics during the Gupta period. Around 500, the astronomer Aryabhata uses the word kha to mark "zero" in tabular arrangements of digits; the 7th century Brahmasphuta Siddhanta contains a comparatively advanced understanding of the mathematical role of zero. The Sanskrit translation of the lost 5th century Prakrit Jaina cosmological text Lokavibhaga may preserve an early instance of positional use of zero.
These Indian developments were taken up in Islamic mathematics in the 8th century, as recorded in al-Qifti's Chronology of the scholars. The numeral system came to be known to both the Persian mathematician Khwarizmi, who wrote a book, On the Calculation with Hindu Numerals in about 825, the Arab mathematician Al-Kindi, who wrote four volumes, On the Use of the Hindu Numerals around 830; these earlier texts did not use the Hindu numerals. Kushyar ibn L
The Suzhou numerals known as Suzhou mazi, is a numeral system used in China before the introduction of Arabic numerals. The Suzhou numerals are known as huama, jingzima and shangma; the Suzhou numeral system is the only surviving variation of the rod numeral system. The rod numeral system is a positional numeral system used by the Chinese in mathematics. Suzhou numerals are a variation of the Southern Song rod numerals. Suzhou numerals were used as shorthand in number-intensive areas of commerce such as accounting and bookkeeping. At the same time, standard Chinese numerals were used in formal writing, akin to spelling out the numbers in English. Suzhou numerals were once popular in Chinese marketplaces, such as those in Hong Kong along with local transportation before the 1990s, but they have been supplanted by Arabic numerals; this is similar to what had happened in Europe with Roman numerals used in ancient and medieval Europe for mathematics and commerce. Nowadays, the Suzhou numeral system is only used for displaying prices in Chinese markets or on traditional handwritten invoices.
In the Suzhou numeral system, special symbols are used for digits instead of the Chinese characters. The digits of the Suzhou numerals are defined between U +3029 in Unicode. An additional three code points starting from U+3038 were added later; the numbers one and three are all represented by vertical bars. This can cause confusion. Standard Chinese ideographs are used in this situation to avoid ambiguity. For example, "21" is written as "〢一" instead of "〢〡" which can be confused with "3"; the first character of such sequences is represented by the Suzhou numeral, while the second character is represented by the Chinese ideograph. The digits are positional; the full numerical notations are written in two lines to indicate numerical value, order of magnitude, unit of measurement. Following the rod numeral system, the digits of the Suzhou numerals are always written horizontally from left to right when used within vertically written documents; the first line contains the numerical values, in this example, "〤〇〢二" stands for "4022".
The second line consists of Chinese characters that represents the order of magnitude and unit of measurement of the first digit in the numerical representation. In this case "十元" which stands for "ten yuan"; when put together, it is read as "40.22 yuan". Possible characters denoting order of magnitude include: qiān for thousand bǎi for hundred shí for ten blank for oneOther possible characters denoting unit of measurement include: yuán for dollar máo or for 10 cents lǐ for the Chinese mile any other Chinese measurement unitNotice that the decimal point is implicit when the first digit is set at the ten position. Zero is represented by the character for zero. Leading and trailing zeros are unnecessary in this system; this is similar to the modern scientific notation for floating point numbers where the significant digits are represented in the mantissa and the order of magnitude is specified in the exponent. The unit of measurement, with the first digit indicator, is aligned to the middle of the "numbers" row.
In the Unicode standard version 3.0, these characters are incorrectly named Hangzhou style numerals. In the Unicode standard 4.0, an erratum was added which stated: The Suzhou numerals are special numeric forms used by traders to display the prices of goods. The use of "HANGZHOU" in the names is a misnomer. All references to "Hangzhou" in the Unicode standard have been corrected to "Suzhou" except for the character names themselves, which cannot be changed once assigned, according to the Unicode Stability Policy. In the episode "The Blind Banker" of the 2010 BBC television series Sherlock, Sherlock Holmes erroneously refers to the number system as "Hangzhou" instead of the correct "Suzhou."
Counting rods are small bars 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any rational number; the written forms based on them are called rod numerals. They are a true positional numeral system with digits for 1–9 and a blank for 0, from the Warring states period to the 16th century. Chinese arithmeticians used counting rods well over two thousand years ago. In 1954 forty-odd counting rods of the Warring States period were found in Zuǒjiāgōngshān Chu Grave No.15 in Changsha, Hunan. In 1973 archeologists unearthed a number of wood scripts from a tomb in Hubei dating from the period of the Han dynasty. On one of the wooden scripts was written: "当利二月定算"; this is one of the earliest examples of using counting-rod numerals in writing. In 1976 a bundle of Western Han-era counting rods made of bones was unearthed from Qianyang County in Shaanxi; the use of counting rods must predate it. The Book of Han recorded: "they calculate with bamboo, diameter one fen, length six cun, arranged into a hexagonal bundle of two hundred seventy one pieces".
At first, calculating rods were round in cross-section, but by the time of the Sui dynasty mathematicians used triangular rods to represent positive numbers and rectangular rods for negative numbers. After the abacus flourished, counting rods were abandoned except in Japan, where rod numerals developed into a symbolic notation for algebra. Counting rods represent digits by the number of rods, the perpendicular rod represents five. To avoid confusion and horizontal forms are alternately used. Vertical rod numbers are used for the position for the units, ten thousands, etc. while horizontal rod numbers are used for the tens, hundred thousands etc. It is written in Sunzi Suanjing that "one is vertical, ten is horizontal". Red rods represent black rods represent negative numbers. Ancient Chinese understood negative numbers and zero, though they had no symbol for the latter; the Nine Chapters on the Mathematical Art, composed in the first century CE, stated " subtract same signed numbers, add different signed numbers, subtract a positive number from zero to make a negative number, subtract a negative number from zero to make a positive number".
A go stone was sometimes used to represent zero. This alternation of vertical and horizontal rod numeral form is important to understanding written transcription of rod numerals on manuscripts correctly. For instance, in Licheng suanjin, 81 was transcribed as, 108 was transcribed as. In the same manuscript, 405 was transcribed as, with a blank space in between for obvious reasons, could in no way be interpreted as "45". In other words, transcribed rod numerals may not be positional, but on the counting board, they are positional. is an exact image of the counting rod number 405 on a table top or floor. The value of a number depends on its physical position on the counting board. A 9 at the rightmost position on the board stands for 9. Moving the batch of rods representing 9 to the left one position gives 9 or 90. Shifting left again to the third position gives 9 or 900; each time one shifts a number one position to the left, it is multiplied by 10. Each time one shifts a number one position to the right, it is divided by 10.
This applies to multiple-digit numbers. Song dynasty mathematician Jia Xian used hand-written Chinese decimal orders 步十百千萬 as rod numeral place value, as evident from a facsimile from a page of Yongle Encyclopedia, he arranged 七萬一千八百二十四 as 七一八二四 萬千百十步He treated the Chinese order numbers as place value markers, 七一八二四 became place value decimal number. He wrote the rod numerals according to their place value: In Japan, mathematicians put counting rods on a counting board, a sheet of cloth with grids, used only vertical forms relying on the grids. An 18th-century Japanese mathematics book has a checker counting board diagram, with the order of magnitude symbols "千百十一分厘毛“. Examples: Rod numerals are a positional numeral system made from shapes of counting rods. Positive numbers are written as they are and the negative numbers are written with a slant bar at the last digit; the vertical bar in the horizontal forms 6–9 are drawn shorter to have the same character height. A circle is used for 0. Many historians think it was imported from Indian numerals by Gautama Siddha in 718, but some think it was created from the Chinese text space filler "□", others think that the Indians acquired it from China, because it resembles a Confucian philosophical symbol for nothing.
In the 13th century, Southern Song mathematicians changed digits for 4, 5, 9 to reduce strokes. The new horizontal forms transformed into Suzhou numerals. Japanese continued to use the traditional forms. Examples: In Japan, Seki Takakazu developed the rod num
Chinese numerals are words and characters used to denote numbers in Chinese. Today, speakers of Chinese use three written numeral systems: the system of Hindu-Arabic numerals used worldwide, two indigenous systems; the more familiar indigenous system is based on Chinese characters that correspond to numerals in the spoken language. These are shared with other languages of the Chinese cultural sphere such as Japanese and Vietnamese. Most people and institutions in China and Taiwan use the Hindu-Arabic or mixed Arabic-Chinese systems for convenience, with traditional Chinese numerals used in finance for writing amounts on checks, some ceremonial occasions, some boxes, on commercials; the other indigenous system is the Suzhou numerals, or huama, a positional system, the only surviving form of the rod numerals. These were once used by Chinese mathematicians, in Chinese markets, such as those in Hong Kong before the 1990s, but have been supplanted by Hindu-Arabic numerals; the Chinese character numeral system consists of the Chinese characters used by the Chinese written language to write spoken numerals.
Similar to spelling-out numbers in English, it is not an independent system per se. Since it reflects spoken language, it does not use the positional system as in Arabic numerals, in the same way that spelling out numbers in English does not. There are characters representing the numbers zero through nine, other characters representing larger numbers such as tens, thousands and so on. There are two sets of characters for Chinese numerals: one for everyday writing, known as xiǎoxiě, one for use in commercial or financial contexts, known as dàxiě; the latter arose because the characters used for writing numerals are geometrically simple, so using those numerals cannot prevent forgeries in the same way spelling numbers out in English would. A forger could change the everyday characters 三十 to 五千 just by adding a few strokes; that would not be possible when writing using the financial characters 叁拾 and 伍仟. They are referred to as "banker's numerals", "anti-fraud numerals", or "banker's anti-fraud numerals".
For the same reason, rod numerals were never used in commercial records. T denotes Traditional Chinese characters. In the People's Liberation Army of the People's Republic of China, some numbers will have altered names when used for clearer radio communications, they are: 0: renamed 洞 lit. Hole 1: renamed 幺 lit. small 2: renamed 两 lit. Double 7: renamed 拐 lit. cane, turn 9: renamed 勾 lit. Hook For numbers larger than 10,000 to the long and short scales in the West, there have been four systems in ancient and modern usage; the original one, with unique names for all powers of ten up to the 14th, is ascribed to the Yellow Emperor in the 6th century book by Zhen Luan, Wujing suanshu. In modern Chinese only the second system is used, in which the same ancient names are used, but each represents a number 10,000 times the previous: In practice, this situation does not lead to ambiguity, with the exception of 兆, which means 1012 according to the system in common usage throughout the Chinese communities as well as in Japan and Korea, but has been used for 106 in recent years.
To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, but uses 万亿 or 太 instead. Due to this, combinations of 万 and 亿 are used instead of the larger units of the traditional system as well, for example 亿亿 instead of 京; the ROC government in Taiwan uses 兆 to mean 1012 in official documents. Numerals beyond 載 zǎi come from Buddhist texts in Sanskrit, but are found in ancient texts; some of the following words may have transferred meanings. The following are characters used to denote small order of magnitude in Chinese historically. With the introduction of SI units, some of them have been incorporated as SI prefixes, while the rest have fallen into disuse. In the People's Republic of China, the early translation for the SI prefixes in 1981 was different from those used today; the larger and smaller Chinese numerals were defined as translation for the SI prefixes as mega, tera, exa, nano, femto, resulting in the creation of yet more values for each numeral.
The Republic of China defined 百萬 as the translation for 兆 as the translation for tera. This translation is used in official documents, academic communities, informational industries, etc. However, the civil broadcasting industries sometimes use 兆赫 to represent "megahertz". Today, the governments of both Taiwan use phonetic transliterations for the SI prefixes. However, the governments have each chosen different Chinese characters for certain prefixes; the following table lists the two different standards together with the early translation. Multiple-digit numbers are constructed using a multiplicative principle. In Mandarin, the multiplier 兩 is used rather than 二 for all numbers 200 and greater with the "2" numeral. Use of both 兩 or 二 are acceptabl
The Brahmi numerals are a numeral system attested from the 3rd century BCE. They are the direct graphic ancestors of the modern Hindu -- Arabic numerals. However, they were conceptually distinct from these systems, as they were not used as a positional system with a zero. Rather, there were separate numerals for each of the tens. There were symbols for 100 and 1000 which were combined in ligatures with the units to signify 200, 300, 2000, 3000, etc; the source of the first three numerals seems clear: they are collections of 1, 2, 3 strokes, in Ashoka's era vertical I, II, III like Roman numerals, but soon becoming horizontal like the modern Chinese numerals. In the oldest inscriptions, 4 is a +, reminiscent of the X of neighboring Kharoṣṭhī, a representation of 4 lines or 4 directions. However, the other unit numerals appear to be arbitrary symbols in the oldest inscriptions, it is sometimes supposed that they may have come from collections of strokes, run together in cursive writing in a way similar to that attested in the development of Egyptian hieratic and demotic numerals, but this is not supported by any direct evidence.
The units for the tens are not related to each other or to the units, although 10, 20, 80, 90 might be based on a circle. The sometimes rather striking graphic similarity they have with the hieratic and demotic Egyptian numerals, while suggestive, is not prima facie evidence of an historical connection, as many cultures have independently recorded numbers as collections of strokes. With a similar writing instrument, the cursive forms of such groups of strokes could be broadly similar as well, this is one of the primary hypotheses for the origin of Brahmi numerals. Another possibility is that the numerals were acrophonic, like the Attic numerals, based on the Kharoṣṭhī alphabet. For instance, chatur 4 early on took a ¥ shape much like the Kharosthi letter ch. However, there are problems of lack of records; the full set of numerals is not attested until 400 years after Ashoka. Assertions that either the numerals derive from tallies or that they are alphabetic are, at best, educated guesses. Brahmi script Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer.
Translated by David Bellos, Sophie Wood, pub. J. Wiley, 2000. Karl Menninger, Number Words and Number Symbols - A Cultural History of Numbers ISBN 0-486-27096-3 David Eugene Smith and Louis Charles Karpinski, The Hindu-Arabic Numerals